Codes and Sequences for Information Retrieval and Stream Ciphers

Given a self-similar structure in codes and de Bruijn sequences, recursive techniques may be used to analyze and construct them. Batch codes partition the indices of code words into m buckets, where recovery of t symbols is accomplished by accessing at most tau in each bucket. This finds use in the retrieval of information spread over several devices. We introduce the concept of optimal batch codes, showing that binary Hamming codes and first order Reed-Muller codes are optimal. Then we study batch properties of binary Reed-Muller codes which have order less than half their length. Cartesian codes are defined by the evaluation of polynomials at a subset of points in F_q. We partition F_q into buckets defined by the quotient with a subspace V. Several properties equivalent to (V intersect ) = {0} for all i,j between 1 and mu are explored. With this framework, a code in F_q^(mu-1) capable of reconstructing mu indices is expanded to one in F_q^(mu) capable of reconstructing mu+1 indices. Using a base case in F_q^3, we are able to prove batch properties for codes in F_q. We generalize this to Cartesian Codes with a limit on the degree mu of the polynomials. De Bruijn sequences are cyclic sequences of length q^n that contain every q-ary word of length n exactly once. The pseudorandom properties of such sequences make them useful for stream ciphers. Under a particular homomorphism, the preimages of a binary de Bruijn sequence form two cycles. We examine a method for identifying points where these sequences may be joined to make a de Bruijn sequence of order n. Using the recursive structure of this construction, we are able to calculate sums of subsequences in O(n^4 log(n)) time, and the location of a word in O(n^5 log(n)) time. Together, these functions allow us to check the validity of any potential toggle point, which provides a method for efficiently generating a recursive specification. Each successful step takes O(k^5 log(k)), for k from 3 to n

On the anomalous afterglow seen in a chameleon afterglow search

We present data from our investigation of the anomalous orange-colored afterglow that was seen in the GammeV Chameleon Afterglow Search (CHASE). These data includes information about the broad band color of the observed glow, the relationship between the glow and the temperature of the apparatus, and other data taken prior to and during the science operations of CHASE. While differing in several details, the generic properties of the afterglow from CHASE are similar to luminescence seen in some vacuum compounds. Contamination from this, or similar, luminescent signatures will likely impact the design of implementation of future experiments involving single photon detectors and high intensity light sources in a cryogenic environment.Comment: 6 pages, 5 figures, submitted to PR

Batch Codes from Hamming and Reed-Muller Codes

Batch codes, introduced by Ishai \textit{et al.}, encode a string $x \in \Sigma^{k}$ into an $m$-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of $t$-users wish to access one bit of information each from the original string. We introduce a concept of optimal batch codes. We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes. We look at locality and availability properties of first order Reed-Muller codes over any finite field. We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Muller codes which have order less than half their length

Batch Codes from Hamming and Reed-Muller Codes

Batch codes, introduced by Ishai \textit{et al.}, encode a string $x \in \Sigma^{k}$ into an $m$-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of $t$-users wish to access one bit of information each from the original string. We introduce a concept of optimal batch codes. We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes. We look at locality and availability properties of first order Reed-Muller codes over any finite field. We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Muller codes which have order less than half their length

Readout process and noise elimination firmware for the Fermilab beam loss system

In the Fermilab Beam Loss Monitor System, inputs from ion chambers are integrated for a short period of time, digitized and processed to create the accelerator abort request signals. The accelerator power supplies employing 3-phase 60Hz AC cause noise at various harmonics on our inputs which must be eliminated for monitoring purposes. During accelerator ramping, both the sampling frequency and the amplitudes of the noise components change. As such, traditional digital filtering can partially reduce certain noise components but not all. A nontraditional algorithm was developed in our work to eliminate remaining ripples. The sequencing in the FPGA firmware is conducted by a micro-sequencer core we developed: the Enclosed Loop Micro-Sequencer (ELMS). The unique feature of the ELMS is that it supports the ''FOR'' loops with pre-defined iterations at the machine code level, which provides programming convenience and avoids many micro-complexities from the beginning